A transistor device having a graphene base for the transport of electrons into a collector is provided. The transistor consists of a heterostructure comprising an electron emitter, an electron collector, and a graphene material base layer consisting of one or more sheets of graphene situated between the emitter and the collector. The transistor also can further include an emitter transition layer at the emitter interface with the base and/or a collector transition layer at the base interface with the collector. The electrons injected into the graphene material base layer can be “hot electrons” having an energy E substantially greater than EF, the Fermi energy in the graphene material base layer or can be “non-hot electrons” having an energy E approximately equal to than EF. The electrons can have the properties of ballistic transit through the base layer.